Microlithography and electron beam writing are examples of applications that generate precise patterns on a sample, such as a semiconductor wafer or mask. Such applications require accurate placement and/or movement of the sample stage relative to the writing tool. Often, accurate positioning of different components within the writing tool, such as the relative position of a reticle in a lithography tool, also requires accurate positioning.
To enable such accurate positioning, heterodyne distance measuring interferometers are often used to measure distance changes along one or more axes. The distance measurements can provide a control signal that drives a servo system for accurately positioning different components of a given system.
A heterodyne distance measuring interferometer measures changes in the position of a measurement object relative to a reference object based on optical interference generated by overlapping and interfering a measurement beam reflected from a measurement object with a reference beam. Measurement of the optical interference produces an interference intensity signal that oscillates at a heterodyne angular frequency xcfx89 corresponding to small difference in frequency between the measurement and reference beams. Changes in the relative position of the measurement object correspond to changes in the phase xcfx86 of the oscillating intensity signal, with a 2xcfx80 phase change substantially equal to a distance change L of xcex/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object, xcex is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects.
Unfortunately, this equality is not always exact. Many interferometers include nonlinearities such as what are known as xe2x80x9ccyclic errors.xe2x80x9d Some cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnL. In particular, the first harmonic cyclic error in phase has a sinusoidal dependence on (2xcfx80pnL)/xcex and the second harmonic cyclic error in phase has a sinusoidal dependence on 2xc2x7(2xcfx80pnL)/xcex. Higher order and sub-harmonic cyclic errors can also be present.
The invention relates to metrology systems in which an interferometric measurement provides a control signal for a servo system that positions a device, such as a lithographic stage. The applicant has recognized that, in the absence of any cyclic error compensation, cyclic errors in the interferometric measurement are a source of a false error signal in the servo system and can cause deviations in the desired position of the device, e.g., stage oscillations. In particular, depending on properties of the complex open-loop gain of the servo system as a function of frequency, the deviations can comprise oscillations with amplitudes that are either as large as the magnitude of the cyclic error(s) in the interferometric measurement or significantly exceed the magnitude of the cyclic error(s). Such deviations, however, provide an observable for identifying and quantifying such cyclic errors. The quantified cyclic errors can be used to generate a compensation signal that corrects the interferometric control signal and thereby eliminating the source of the false error signal in the servo system and improves the accuracy of the stage metrology system.
In general, in one aspect, the invention features a method for determining nonlinear cyclic errors in a metrology system that positions a measurement object (e.g., a stage in a lithography or beam writing tool) under servo-control based on an interferometrically derived position signal. The method includes: translating the measurement object under servo-control at a fixed speed; identifying frequencies of any oscillations on the position of measurement object as it is translated at the fixed speed; and determining amplitude and phase coefficients for a sinusoidal correction term at one of the identified frequencies which when combined with the position signal suppress the oscillations at that frequency.
Embodiments of the method may further include any of the following features.
The method may further include the steps of: repeating the translating, identifying, and determining steps for each of multiple, additional fixed speeds; and generating a representation of the nonlinear cyclic errors based on the coefficients and identified frequencies corresponding to the oscillations at each of the fixed speeds.
In some embodiments, the interferometrically derived position signal is the phase of an interferometric intensity signal at a heterodyne frequency. In other embodiments, the interferometrically derived position signal is a heterodyne, interferometric intensity signal.
To combine the sinusoidal correction signal with the position signal, the sinusoidal correction term may be, for example, subtracted from or added to the position signal to suppress the oscillations.
In general, in another aspect, the invention features a method for positioning a measurement object (e.g., a stage in a lithography or beam writing tool) under servo-control based on an interferometrically derived position signal indicative of a position for the measurement object. The method includes: generating a compensated position signal based on the interferometrically derived position signal and at least one correction term that has a sinusoidal dependence on the position of the measurement object; and repositioning the measurement object based on the compensated position signal and a desired position for the measurement object.
Embodiments of the method may include any of the following features.
For example, the generation of the compensated position signal may include: determining a speed for the measurement object based on the interferometrically derived position signal, and selecting parameters for the at least one sinusoidal correction term based on the determined speed.
The compensated position signal may be generated by subtracting the at least one sinusoidal correction term from the interferometrically derived position signal.
The interferometrically derived position signal may be the phase of an interferometric intensity signal at a heterodyne frequency. Alternatively, the interferometrically derived position signal may be a heterodyne, interferometric intensity signal.
The at least one sinusoidal correction term may include multiple sinusoidal correction terms (e.g., two, three, or more such terms). Each of the multiple sinusoidal correction terms may correspond to a cyclic error in the interferometrically derived position signal.
In general, in another aspect, the invention features an electronic processing system for use with a servo-system for positioning a measurement object. The electronic processing system includes: an input port configured to receive a position signal from an interferometry system indicative of a position for the measurement object; a memory storing a representation of nonlinear errors in the interferometry system; a processor which during operation generates a compensated position signal based on the position signal from the interferometry system and the stored representation; and an output port configured to direct the compensated position signal to a servo-controller.
Embodiments of the electronic processor may include any of the following features.
For example, the stored representation of nonlinear errors may be expressed as a sum of multiple correction terms each having a sinusoidal dependence on the position of the measurement object.
The stored representation of nonlinear errors may be parameterized by a speed of the measurement object. For example, during operation the processor may further determine an estimate for the speed of the measurement object based on the position signal from the interferometry system, and generate the compensated position signal based on the position signal from the interferometry system, the stored representation of nonlinear errors, and the estimated speed.
Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.